Running head: PROPORTIONAL REASONING
1
Proportional Reasoning Activity
Kimberly M. Willis
Walden University
Amy Gaskins
Algebraic Reasoning, Functions, and Equations MATH- 6553A
July 27, 2014

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PROPORTIONAL REASONING
2
Proportional Reasoning
Proportional reasoning cannot be taught (or learned) in one lesson but must be developed
through activities.
Like equivalence, proportional reasoning is considered to be a unifying theme
in mathematics because it is not simply how to set up a proportion to solve a problem but rather a
way of reasoning about situations (Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M..
2013).
Because proportional reasoning requires a true understanding, rather than simply using
an algorithm, this ability is developed throughout the course of several years beginning in
elementary school.
In sixth grade, students are still developing an understanding of ratios and proportions.
I
find it very important for students to use manipulatives and a variety of strategies to solve the
problems.
I try to stay away from the algorithm as long as possible because I feel that the
algorithm is not really necessary if the students have a strong understanding of proportions.
In
this lesson, I started by giving students cubes with two different colors (I gave blue and black).
I
presented them with the problem,
A package of pens contains one blue pen and four black pens.
Use your cubes to model this situation.
I figured this was a good way to introduce probability.
Students have set up a ratio of blue to black pens without even realizing it.
Next, I took it one
step further and asked the students what would happen if there were two packs.
Some students
immediately wanted to tell me that I would have twice as many blue and black pens.
I had
students model their thoughts using the cubes.
Students have now found equivalent ratios still
without even mentioning ratios or proportions.
Next, I allowed the students a little more
freedom by asking them what other amounts of each color pen they would have if they bought
more packs.
I allowed the students time to experiment and come up with several different
answers.
Students then had the opportunity to share different answers with their classmates and

PROPORTIONAL REASONING
3
we kept a list on the board on chart paper.
I save this list so that we can refer back to it in future
lesssons.
The last part of this first activity required students to work backwards to solve this
problem.
They were challenged to find out how many blue pens the secretary ordered if she
ordered a total of 42 pens.
Students who are able to study mathematics and work inversely to
make links with their prior knowledge have a much deeper understanding of the material they are
learning.
As the students worked together on similar scenarios, I encouraged them to use different
methods.
In the beginning, students used the cubes.
I then began to see students using drawings,
symbols, repeated addition, multiplication and division.
I was excited with the number of
methods they used.

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- Fall '14